So it's probably time to put this to bed. No, the vendor for the heatsinks didn't swap them out; they just refunded my money once they got them back. Ordered a pair from another vendor, they arrived quickly, and were the correct parts. So today was the big day.
Replacing the old mobo with the new wasn't too tough. I needed to move two of the standoffs in the chassis, but once I did, everything fit nicely. Props to Supermicro for making that relatively painless. Then it was update BIOS (or "embedded motherboard firmware", if you like), then update BMC, then update HBA firmware. Then futz with the boot order settings in the BIOS to get it to boot from the right device. The only problem I ran into is that apparently those "predictable network interface names" aren't, so now the two ports on my Chelsio NIC are enp94s0f4 and enp94s0f4d1 rather than whatever they were before. So destroy the LAGG interface, recreate it with the two correct ports, and it's all good.
So everything's up and running. And now I have a HTML5 virtual console, which will make it much easier to remote-admin the thing in the future. And it seems to be running the fans a little slower, which I don't mind, even though the server room is now far enough from the house that it doesn't much matter any more. I'll want to make sure temps stay reasonable, but
Now if only upgraded CPUs for my MicroServer Gen10+ were more reasonably priced...
Edit: the newer IPMI firmware also means that it's easier to update its TLS certificate, and even to automate that using a script like this:
https://gist.github.com/arnebjarne/54dbab54e5fb82043a4835c0250840b4. If you're using the SmallStep CA software to run a local CA, make sure to issue the cert using a RSA key rather than EC, as the firmware apparently doesn't support EC certs.